Tag Archives: Back of the envelope

I often listen to music or use my phone while walking through town. I have heard that this is dangerous and could cause me to get killed, so I’ll attempt a back of the envelope calculation to work out if I should stop.

Firstly, the base rate of risk for being run over as a pedestrian in the UK is 0.0006% per person each year. Let’s say as a young man I face double that risk, or 0.0012%. I don’t know how much using my phone some of the time while walking raises the risk, though this data suggests a pedestrian failing to look properly was the cause of 190 road fatalities in the UK, out of a total of 385 pedestrian deaths. For the sake of argument, let’s say the risk triples. Let me know if you have a better estimate. That would result in an extra risk of death of 0.0024% each year. Dying now would cost me some 60 years of healthy life, so I should expect to lose 0.00144 years for each year I engage in this behaviour – which is around 12 hours.

As compensation, I get to listen to music, audiobooks and check my email for on average 10 minutes a day, which comes to 60 hours or so a year. I would say that time is about 50% better spend than it would be otherwise thanks to my ability to use my phone, so I expect to gain the equivalent of 30 hours a year.

If these numbers are about right, I should be fairly comfortable listening to music or looking at my phone as a pedestrian. However, the harm is pretty close to the benefit, and someone could reasonably think the cost actually outweighs the benefit.

Nonetheless I could do better by not using my phone in cases where the cost exceeds the benefit, for example by keeping the volume low, not having conversations which are particularly distracting, and being strict about not starting to look at my phone if I expect to cross the street soon after.

If you like this approach – and maybe even if you don’t – you’ll also like How to Gain or Lose 30 Minutes of Life Every Day, which estimates how much life you should expect to gain or lose each time you exercise, eat fruit, vegetables or meat, drink alcohol, smoke a cigarette, remain overweight, or sit at a computer for hours at a time. Gains and losses are measured using the ‘micromort‘, which corresponds to half an hour of life. While the numbers are no doubt a dramatic simplification of the medical evidence, I find a concrete estimate of the benefits gives me stronger motivation to eat more vegetables, drink less, and perhaps exercise more as well. And it helps me prioritise which health enhancing activities are worth the trouble, and which are not.

After the shocking massacre in Connecticut it looks like gun control is going to draw a lot of attention from Obama and Congress this year. This got me thinking about how important gun control might be as a political cause. The potential good achieved by focussing on this policy is in large part determined by the damage done by guns in the first place. In that light, does it deserve it?

A natural measure of the importance of the problem is the number of years of healthy life lost due to gun violence. At the moment there are a bit over 8,000 murders with firearms each year in the US, some two thirds of the total. If we guess that the typical age of death from gun violence is 30, then the average survivor would have enjoyed another 50 years or so of healthy life. Firearm homicides would than lead to the loss of 400,000 years of healthy life each year. We would then have to add health problems among survivors of gun violence. To confirm that these figures are sensible I looked up the World Health Organisation’s Global Burden of Disease, which suggest ‘intentional violence’ as a whole cost the US and Canada about 1,100,000 years of healthy life each year. Two thirds of this would be 650,000 years, a figure which amounts to about 0.8% of the total burden of disease and injury in the US.

Another even larger problem than murder – at least as far as years of healthy life lost – is suicide. Easy access to guns makes suicide attempts more likely to succeed. The US suicide rate is 12 per 100,000; tragically high, though sadly unexceptional by international standards. If the typical suicide victim would have lived another 45 healthy years, this amounts to an annual burden of 1,600,000 each year, roughly the WHO’s figure. [1] Firearms are used for about half of these suicides, so we’ll say they have a burden of 800,000 years of healthy life, or about 1% of the total burden of disease and injury.

How much could the US hope to reduce these figures? Of course the relationship between the number of guns and violence is contested, and I don’t really want to get drawn into that debate. I will just assume, for the sake of argument, that gun control policies could indeed help reduce violence. For that purpose, let’s imagine it could get firearm violence and suicide down to the average of other OECD countries. [1] Doing so would reduce the gun death rate (and I will assume injuries too) by 80% from ~10 to ~2 per 100,000. This is wildly optimistic given the other drivers of violence and suicide in the US, and the timidity of any likely gun control laws under the Second Amendment. Even if guns did become hard to access, we would expect to see substitution to other weapons. Nonetheless, it offers a useful upper bound.

An 80% drop in firearm deaths and injuries would prevent the loss of 1.15 million years of healthy life each year, or around 1.4 per cent of all the damage done by disease and injury in the US. This falls inconveniently between ‘very little’ and ‘quite a bit’. How can we put this figure in perspective? One option would be to consider how much people claim to value their lives, while another would be to compare it to other available options for saving lives. Here I will use the latter to give some idea of how focussing on gun control compares to other policies or causes that might improve the health of Americans.

How much does it cost to save a life in the US? The NHS in Britain conveniently uses £30,000 (around $US50,000) for each year of healthy life as the highest price at which a treatment is worth funding. The US has no central body for making these decisions, so no generic ‘marginal cost’ exists. A conclusion of the classic paper, Five-hundred life-saving interventions and their cost-effectiveness, is that the cost of extending lives varies across several orders of magnitude depending on the approach you take. Nonetheless, many interventions in medicine and general safety fell between $5-50,000 for a year of life, at least in the mid-90s. A quick search turns up vaccination of US girls against HPV, which buys a year of healthy life for about $44,000, total knee arthroplasty for $18,300, HIV screening for under $25,000 and flu vaccination at $8,000-52,000. The availability of all of these could be expanded. At a rounded $50,000 figure, the equivalent of 1.15 million years of healthy life could be saved for $57 billion, or 0.38% of US GDP – a significant sum, though under a fifth of long run annual growth. By comparison, the US Federal Government already spends about 24% of US GDP, and all healthcare spending accounts for some 15%. Based on Robin’s work on the inefficacy of much US healthcare spending, redirecting some of that enormous budget to truly life-saving activities would go a long way.

If American activists or voters currently preoccupied with gun control were willing to look farther afield in their desire to prevent unnecessary death, directing government spending to provide bed nets to protect children in developing countries against malaria could save 30,000 kids for a meagre $70 million, or 0.00000046% of GDP. Sadly, the effectiveness and size of US foreign aid is barely discussed.

Of course this health story is not the full picture of the damage done by gun violence. We ought also consider the:

Costs incurred in trying to stay safe

Costs of caring for the injured

Loss of human capital from adults dying

Resulting distress and fear

Reduced urbanisation as a result of crime (which lowers productivity, among other things).

I would appreciate attempts to quantify these costs but don’t have time to pursue them myself right now. I would note in passing that many other interventions that improve health and safety would also reduce these harms to some extent.

My interpretation of the above is that gun violence is a serious issue in the US. It is not being blown out of proportion like shark attacks or terrorism. At the same time, the impact of guns on US health-span is modest, and lower than many common and avoidable diseases or accidents which fail to inspire a national conversation. Guns have become a hot issue because of their grisly and visible results, as well as fierce identity politics, rather than the absolute scale of the damage they do. If the main goal of gun control advocates were to save lives, their cause would not stand out as low-hanging fruit, especially if they cared about foreigners as well as Americans. Given the host of major problems facing the US, the limited attention of Congress and the White House, and the improbability of achieving a significant reduction in the number of dangerous weapons available, it is not a cause I would jump on.

[1] Some would say that a death by suicide isn’t as bad as a murder, because someone who is preventing from committing suicide probably has a low quality of life. There is some truth to this but I will ignore it, consistent with my desire to define an upper bound.